Hands-on Exercise 4

This hands-on exercise covers the appropriate functions of spatstat package to perform spatial point patterns analysis.

Genice Goh true
09-15-2021

Installing and Loading Packages

packages = c('sf', 'spatstat', 'raster', 'maptools', 'tmap')
for (p in packages){
  if(!require(p, character.only = T)){
    install.packages(p)
  }
  library(p,character.only = T)
}

Spatial Data Wrangling

Importing spatial data

st_read() of sf package is used to import the geospatial data

childcare_sf <- st_read("data/child-care-services-geojson.geojson") %>%
  st_transform(crs=3414)
Reading layer `child-care-services-geojson' from data source 
  `C:\Users\user\Desktop\SMU\Y4S1\IS415\geniceee\IS415_blog\_posts\2021-09-15-hands-on-exercise-4\data\child-care-services-geojson.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
sg_sf <- st_read(dsn = "data", layer="CostalOutline")
Reading layer `CostalOutline' from data source 
  `C:\Users\user\Desktop\SMU\Y4S1\IS415\geniceee\IS415_blog\_posts\2021-09-15-hands-on-exercise-4\data' 
  using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21
mpsz_sf <- st_read(dsn = "data", 
                   layer = "MP14_SUBZONE_WEB_PL")
Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\Users\user\Desktop\SMU\Y4S1\IS415\geniceee\IS415_blog\_posts\2021-09-15-hands-on-exercise-4\data' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

Important to ensure that sg_sf and mpsz_sf are projected in the same projection system before using these data for analysis

print(st_crs(sg_sf))
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]
print(st_crs(mpsz_sf))
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]

Although both sg_sf and mpsz_sf are projected in SVY21, the end of both prints indicate that the EPSG is 9001. This is a wrong EPSG code because the correct EPSG code for SVY21 should be 3414. There is therefore a need to assign the correct EPSG codes to sg_sf and mpsz_sf.

sg3414_sf <- st_set_crs(sg_sf, 3414)

mpsz3414_sf <- st_set_crs(mpsz_sf, 3414)

Mapping the geospatial datasets

It is useful to plot a map to show the geospatial data’s spatial patterns

tm_shape(sg_sf) +
  tm_polygons() +
tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(childcare_sf)+
  tm_dots()

Note: All the geospatial layers are within the same map extend. This shows that their referencing system and coordinate values are referring to similar spatial context

Alternatively, a pin map can be plotted. Its advantages are:

tmap_mode('view')
tm_shape(childcare_sf)+
  tm_dots()
tmap_mode('plot')

Note: Always remember to switch back to plot mode afterwards because each interactive mode will consume a connection. Avoid displaying too many interactive maps in 1 RMarkdown document when publishing on Netlify.

Geospatial Data Wrangling

Many geospatial analysis packages require the input geospatial data in sp’s Spatial* classes

Converting sf data frames to sp’s Spatial* class

as_Spatial() of sf package is used to convert the data from sf data frame to sp’s Spatial* class

childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz3414_sf)
sg <- as_Spatial(sg3414_sf)
childcare
class       : SpatialPointsDataFrame 
features    : 1545 
extent      : 11203.01, 45404.24, 25667.6, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 2
names       :    Name,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Description 
min values  :   kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>018989</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>1, MARINA BOULEVARD, #B1 - 01, ONE MARINA BOULEVARD, SINGAPORE 018989</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>THE LITTLE SKOOL-HOUSE INTERNATIONAL PTE. LTD.</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>08F73931F4A691F4</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
max values  : kml_999,                  <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>829646</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>200, PONGGOL SEVENTEENTH AVENUE, SINGAPORE 829646</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>RAFFLES KIDZ @ PUNGGOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>379D017BF244B0FA</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
mpsz
class       : SpatialPolygonsDataFrame 
features    : 323 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 15
names       : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C,          INC_CRC, FMEL_UPD_D,     X_ADDR,     Y_ADDR,    SHAPE_Leng,    SHAPE_Area 
min values  :        1,          1, ADMIRALTY,    AMSZ01,      N, ANG MO KIO,         AM, CENTRAL REGION,       CR, 00F5E30B5C9B7AD8,      16409,  5092.8949,  19579.069, 871.554887798, 39437.9352703 
max values  :      323,         17,    YUNNAN,    YSSZ09,      Y,     YISHUN,         YS,    WEST REGION,       WR, FFCCF172717C2EAF,      16409, 50424.7923, 49552.7904, 68083.9364708,  69748298.792 
sg
class       : SpatialPolygonsDataFrame 
features    : 60 
extent      : 2663.926, 56047.79, 16357.98, 50244.03  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 4
names       : GDO_GID, MSLINK, MAPID,              COSTAL_NAM 
min values  :       1,      1,     0,             ISLAND LINK 
max values  :      60,     67,     0, SINGAPORE - MAIN ISLAND 

Converting the Spatial* class into generic sp format

spatstat requires the data to be in ppp object form. To convert Spatial* class to ppp object, the Spatial* class needs to be convert into Spatial object first.

childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")
childcare_sp
class       : SpatialPoints 
features    : 1545 
extent      : 11203.01, 45404.24, 25667.6, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
sg_sp
class       : SpatialPolygons 
features    : 60 
extent      : 2663.926, 56047.79, 16357.98, 50244.03  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

Converting generic sp format into spatstat’s ppp format

as.ppp()of spatstat is used to convert the Spatial object into spatstat’s ppp object format

childcare_ppp <- as(childcare_sp, "ppp")
childcare_ppp
Planar point pattern: 1545 points
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units


Plotting childcare_ppp

plot(childcare_ppp)


Summary statistics of childcare_ppp

summary(childcare_ppp)
Planar point pattern:  1545 points
Average intensity 1.91145e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
                    (34200 x 23630 units)
Window area = 808287000 square units

Note: In spatial point patterns analysis, the presence of duplicates is a significant issue. The statistical methodology used for spatial point patterns processes is based largely on the assumption that the process is simple (i.e. the points cannot be coincident)

Handling duplicated points

Check for any duplication in childcare_ppp

any(duplicated(childcare_ppp))
[1] TRUE

multiplicity() is used to count number of coincidence points. To know how many locations have >1 point event, refer to code chunk below:

sum(multiplicity(childcare_ppp) > 1)
[1] 128

The output shows that there are 128 duplicated points. Plotting the data will allow us to view their locations

tmap_mode('view')
tm_shape(childcare) +
  tm_dots(alpha=0.4, 
          size=0.05)
tmap_mode('plot')

To overcome this problem:

Implementing Jittering Approach

childcare_ppp_jit <- rjitter(childcare_ppp, 
                             retry=TRUE, 
                             nsim=1, 
                             drop=TRUE)

There are no duplicate points now

any(duplicated(childcare_ppp_jit))
[1] FALSE

Creating owin object

Good practice to confine the analysis within a geographical area when doing spatial point patterns analysis. In spatstat, an object called owin is specially designed to represent this polygonal region

sg_owin <- as(sg_sp, "owin")

plot(sg_owin)

Combining point events object and owin object

Extract childcare centres that are located within Singapore

childcareSG_ppp = childcare_ppp[sg_owin]


The output object combined both the point and polygon feature in 1 ppp object class

summary(childcareSG_ppp)
Planar point pattern:  1545 points
Average intensity 2.063463e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: polygonal boundary
60 separate polygons (no holes)
            vertices        area relative.area
polygon 1         38 1.56140e+04      2.09e-05
polygon 2        735 4.69093e+06      6.27e-03
polygon 3         49 1.66986e+04      2.23e-05
polygon 4         76 3.12332e+05      4.17e-04
polygon 5       5141 6.36179e+08      8.50e-01
polygon 6         42 5.58317e+04      7.46e-05
polygon 7         67 1.31354e+06      1.75e-03
polygon 8         15 4.46420e+03      5.96e-06
polygon 9         14 5.46674e+03      7.30e-06
polygon 10        37 5.26194e+03      7.03e-06
polygon 11        53 3.44003e+04      4.59e-05
polygon 12        74 5.82234e+04      7.78e-05
polygon 13        69 5.63134e+04      7.52e-05
polygon 14       143 1.45139e+05      1.94e-04
polygon 15       165 3.38736e+05      4.52e-04
polygon 16       130 9.40465e+04      1.26e-04
polygon 17        19 1.80977e+03      2.42e-06
polygon 18        16 2.01046e+03      2.69e-06
polygon 19        93 4.30642e+05      5.75e-04
polygon 20        90 4.15092e+05      5.54e-04
polygon 21       721 1.92795e+06      2.57e-03
polygon 22       330 1.11896e+06      1.49e-03
polygon 23       115 9.28394e+05      1.24e-03
polygon 24        37 1.01705e+04      1.36e-05
polygon 25        25 1.66227e+04      2.22e-05
polygon 26        10 2.14507e+03      2.86e-06
polygon 27       190 2.02489e+05      2.70e-04
polygon 28       175 9.25904e+05      1.24e-03
polygon 29      1993 9.99217e+06      1.33e-02
polygon 30        38 2.42492e+04      3.24e-05
polygon 31        24 6.35239e+03      8.48e-06
polygon 32        53 6.35791e+05      8.49e-04
polygon 33        41 1.60161e+04      2.14e-05
polygon 34        22 2.54368e+03      3.40e-06
polygon 35        30 1.08382e+04      1.45e-05
polygon 36       327 2.16921e+06      2.90e-03
polygon 37       111 6.62927e+05      8.85e-04
polygon 38        90 1.15991e+05      1.55e-04
polygon 39        98 6.26829e+04      8.37e-05
polygon 40       415 3.25384e+06      4.35e-03
polygon 41       222 1.51142e+06      2.02e-03
polygon 42       107 6.33039e+05      8.45e-04
polygon 43         7 2.48299e+03      3.32e-06
polygon 44        17 3.28303e+04      4.38e-05
polygon 45        26 8.34758e+03      1.11e-05
polygon 46       177 4.67446e+05      6.24e-04
polygon 47        16 3.19460e+03      4.27e-06
polygon 48        15 4.87296e+03      6.51e-06
polygon 49        66 1.61841e+04      2.16e-05
polygon 50       149 5.63430e+06      7.53e-03
polygon 51       609 2.62570e+07      3.51e-02
polygon 52         8 7.82256e+03      1.04e-05
polygon 53       976 2.33447e+07      3.12e-02
polygon 54        55 8.25379e+04      1.10e-04
polygon 55       976 2.33447e+07      3.12e-02
polygon 56        61 3.33449e+05      4.45e-04
polygon 57         6 1.68410e+04      2.25e-05
polygon 58         4 9.45963e+03      1.26e-05
polygon 59        46 6.99702e+05      9.35e-04
polygon 60        13 7.00873e+04      9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
                     (53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414


Plot the newly derived childcareSG_ppp

plot(childcareSG_ppp)

First-order Spatial Point Patterns Analysis

Kernel Density Estimation

Kernel density can be computed with density() of spatstat using the following configurations:

kde_childcareSG_bw <- density(childcareSG_ppp,
                              sigma=bw.diggle,
                              edge=TRUE,
                            kernel="gaussian") 

plot(kde_childcareSG_bw)

The output density values are way too small to comprehend. This is because the default unit of measurement of SVY21 is in m. As a result, the density values computed is in number of points/square metre


Retrieve bandwidth used to compute KDE layer

bw <- bw.diggle(childcareSG_ppp)
bw
   sigma 
298.4095 

Rescaling KDE values

rescale() is used to covert the unit of measurement from m to km

childcareSG_ppp.km <- rescale(childcareSG_ppp, 1000, "km")


Re-run density() using the rescaled data set and plot the output KDE map

kde_childcareSG.bw <- density(childcareSG_ppp.km, 
                              sigma=bw.diggle, 
                              edge=TRUE, 
                              kernel="gaussian")
plot(kde_childcareSG.bw)

Note: Output image looks identical to the earlier version, the only changes are in the data values

Working with different automatic bandwidth methods

Besides bw.diggle(), 3 other spatstat functions can be used to determine the bandwidth: bw.CvL(), bw.scott(), and bw.ppl().

Look at the bandwidth return by these automatic bandwidth calculation methods:

bw.CvL(childcareSG_ppp.km)
   sigma 
4.543278 
bw.scott(childcareSG_ppp.km)
 sigma.x  sigma.y 
2.224898 1.450966 
bw.ppl(childcareSG_ppp.km)
    sigma 
0.3897114 
bw.diggle(childcareSG_ppp.km)
    sigma 
0.2984095 

bw.ppl() is suggested because it tends to produce more appropriate values when the pattern consists predominantly of tight clusters. However, if the purpose is to detect a single tight cluster in the midst of random noise, then bw.diggle() method seems to work best

kde_childcareSG.ppl <- density(childcareSG_ppp.km, 
                               sigma=bw.ppl, 
                               edge=TRUE,
                               kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")

6.1.3 Working with different kernel methods

By default, the kernel method used in density.ppp() is gaussian. There are three other options: Epanechnikov, Quartic and Dics

par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="gaussian"), 
     main="Gaussian")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="epanechnikov"), 
     main="Epanechnikov")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="quartic"), 
     main="Quartic")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="disc"), 
     main="Disc")

Fixed and Adaptive KDE

Computing KDE with fixed bandwidth

We will now compute a KDE layer by defining a bandwidth of 600m. Sigma value used is 0.6 because km is the unit of measurement for childcareSG_ppp.km

kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)

Computing KDE with adpative bandwidth

Fixed bandwidth method is very sensitive to highly skew distribution of spatial point patterns over geographical units. Use adaptive bandwidth to overcome this issue

density.adaptive() of spatstat is used to derive adaptive kernel density estimation

kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)

Compare fixed and adaptive kernel density estimation outputs

par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")

Converting KDE output into grid object

The result is the same, we just convert it so that it is suitable for mapping purposes

gridded_kde_childcareSG_bw <- as.SpatialGridDataFrame.im(kde_childcareSG.bw)
spplot(gridded_kde_childcareSG_bw)

Converting Gridded Output into Raster

raster() of raster package is used to convert the gridded kernel density objects into RasterLayer object

kde_childcareSG_bw_raster <- raster(gridded_kde_childcareSG_bw)

Properties of kde_childcareSG_bw_raster RasterLayer

Note that the CRS property is NA

kde_childcareSG_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348  (x, y)
extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
crs        : NA 
source     : memory
names      : v 
values     : -8.476185e-15, 28.51831  (min, max)

Assigning Projection Systems

CRS information will now be included in kde_childcareSG_bw_raster RasterLayer Note that the crs property is completed

projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348  (x, y)
extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
crs        : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs 
source     : memory
names      : v 
values     : -8.476185e-15, 28.51831  (min, max)

Visualising the output in tmap

tm_shape(kde_childcareSG_bw_raster) + 
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

Note: raster values are encoded explicitly onto the raster pixel using the values in “v” field

Comparing Spatial Point Patterns using KDE

KDE of childcare centres will be compared at Ponggol, Tampines, Chua Chu Kang and Jurong West planning areas

Extracting Study Area

pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]

par(mfrow=c(2,2))
plot(pg, main = "Ponggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")

Converting spatial point data frame into generic sp format

Convert SpatialPolygonsDataFrame layers into generic spatialpolygons layers

pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")
6.1.7.4 Creating Owin Object

Convert these SpatialPolygons objects into owin objects required by spatstat

pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")

Combining childcare points and the study area

Extract childcare centres within the regions for later analysis

childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]

rescale() is used to trasnform the unit of measurement from m to km

childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")

par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")

Computing KDE

bw.diggle method is used to derive the bandwidth of each KDE

par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tempines")
plot(density(childcare_ck_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Jurong West")

Computing fixed bandwidth KDE

par(mfrow=c(2,2))
plot(density(childcare_ck_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Chou Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Jurong West")
plot(density(childcare_pg_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tampines")

Nearest Point Analysis

clarkevans.test() of statspat is used to perform Clark-Evans test of aggregation for a spatial point pattern

The test hypotheses are:

The 95% confident interval will be used

Testing spatial point patterns using Clark and Evans Test

clarkevans.test(childcareSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Monte Carlo test based on 99 simulations of CSR with fixed n

data:  childcareSG_ppp
R = 0.54756, p-value = 0.01
alternative hypothesis: clustered (R < 1)

Conclusion: Since p-value is less than 0.05, we can therefore reject the null hypothesis that distribution of childcare services are randomly distributed. Since the Nearest Neighbour index is < 1, we can infer that the distribution of childcare services resemble a clustered distribution

Clark and Evans Test: Choa Chu Kang planning area

clarkevans.test() of spatstat is used to performs Clark-Evans test of aggregation for childcare centres in Choa Chu Kang planning area

clarkevans.test(childcare_ck_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Monte Carlo test based on 999 simulations of CSR with fixed n

data:  childcare_ck_ppp
R = 0.97247, p-value = 0.194
alternative hypothesis: two-sided

Clark and Evans Test: Tampines planning area

clarkevans.test(childcare_tm_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Monte Carlo test based on 999 simulations of CSR with fixed n

data:  childcare_tm_ppp
R = 0.78065, p-value = 0.002
alternative hypothesis: two-sided

Spatial Second-order Spatial Point Patterns Analysis

Analysing Spatial Point Process Using G-Function

G function measures the distribution of the distances from an arbitrary event to its nearest event. Gest() and envelope() of spatstat() package is used to compute G-function estimation and perform monte carlo simiulation respectively

Choa Chu Kang planning area

Computing G-Function Estimation

Gest() of spatstat package is used to compute G function

G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK, xlim=c(0,500))

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

Monte Carlo test with G-function

G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.

Done.
plot(G_CK.csr)

Tampines planning area

Computing G-Function Estimation

G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.

Done.
plot(G_tm.csr)

Analysing Spatial Point Process Using F-Function

F function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape. Fest() and envelope() of spatstat() package is used to compute F-function estimation and perform monte carlo simiulation respectively

Choa Chu Kang planning area

Computing F-Function Estimation

Fest() of spatstat package is used to compute F-function

F_CK = Fest(childcare_ck_ppp)
plot(F_CK)

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

Monte Carlo test with F-function

F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.

Done.
plot(F_CK.csr)

Tampines planning area

Computing F-Function Estimation

F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.

Done.
plot(F_tm.csr)

Analysing Spatial Point Process Using K-Function

K-function measures the number of events found up to a given distance of any particular event. Kest() and envelope() of spatstat() package is used to compute K-function estimation and perform monte carlo simiulation respectively

Choa Chu Kang planning area

Computing K-Function Estimate

K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

Performing Complete Random Spatial Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Tampines planning area

Computing K-Function Estimation

K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r, 
     ylab= "K(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

Performing Complete Random Spatial Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(K_tm.csr, . - r ~ r, 
     xlab="d", ylab="K(d)-r", xlim=c(0,500))

Analysing Spatial Point Process Using L-Function

Lest() and envelope() of spatstat package is used to compute L-function estimation and perform monte carlo simulation test respectively

Choa Chu Kang planning area

####Computing L-Function Estimation

L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Random Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

Tampines planning area

Computing L-Function Estimate

L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

Performing Complete Spatial Random Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted:

The null hypothesis will be rejected if p-value < 0.001 (alpha value)

L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(L_tm.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))